Network Diagrams from Precedence Tables
Learn to build and read network diagrams from precedence tables for NSW Year 12 Mathematics Standard 2. In this critical-path topic every activity is drawn as a directed arrow and every numbered circle is an event, so a table of activities and their immediate predecessors becomes an activity-on-edge network.
You will construct a network from a precedence table, identify the starting and finishing activities, read the immediate predecessors straight off the diagram, and insert a dummy activity where a shared dependency requires one — the foundation for critical path analysis in Standard 2.
Theory
Network diagrams from precedence tables turn a list of activities and their predecessors into an activity-on-edge diagram. This Year 12 Standard 2 (NSW) guide shows how to construct and read one — activities as arrows, events as circles, the immediate predecessors, the starting and finishing activities, and when a dummy activity is needed.
A precedence table lists the activities in a project and, for each one, its immediate predecessors — the activities that must be finished first. A dash (—) means an activity has no predecessor and can start straight away.
An activity-on-edge (AoE) network draws the same information as a diagram. Every activity is a directed arrow, and every numbered circle is an event — a point in time where activities finish and others begin. The arrow directions show the order the work must happen in.
Reading the network back: the immediate predecessors of an activity are the arrows entering the event where it begins. Activities that leave the start event are the starting activities; an activity reaching the final event with nothing after it is a finishing activity. A dummy activity (a dashed arrow, no work and zero time) is added only to keep the predecessor logic correct.
There are no formulas to memorise — instead there are two reading rules that turn the picture into predecessor logic and back.
Whether an activity starts or finishes the project is read the same way:
How to construct the network from a precedence table
- List the activities and read each one's immediate predecessors from the table.
- Start: draw every activity with a dash leaving the single start event.
- Attach each remaining activity so it leaves the event where all of its predecessors finish.
- Dummy check: if two activities share only some predecessors (or would share the same pair of events), add a dashed dummy so each has exactly the right predecessors.
- Finish and check: lead the last activities to a final event, then read the network back to confirm every predecessor matches the table.
Count the arrows, then read what enters each event.
| \(\text{arrows } A\text{--}F\) | \(=\) | \(6\text{ activities}\) |
| \(\text{leave event } 1\) | \(:\) | \(A,\ B\) |
| \(\text{enter } E\text{'s event}\) | \(:\) | \(B,\ C\) |
Read the arrows entering \(G\), then find which arrows reach the final event.
| \(\text{enter } G\text{'s event}\) | \(:\) | \(D,\ E\) |
| \(\text{reach final event}\) | \(:\) | \(F,\ G\) |
| \(\therefore\ \text{finish}\) | \(=\) | \(F,\ G\) |
| Activity | Immediate predecessor(s) |
|---|---|
| \(A\) | — |
| \(B\) | — |
| \(C\) | A |
| \(D\) | B |
| \(E\) | C, D |
| \(F\) | E |
\(A\) and \(B\) start; build each activity after its predecessors.
| \(A,\ B\) | \(:\) | \(\text{dash} \Rightarrow \text{start}\) |
| \(C\text{ after }A\) | \(,\) | \(D\text{ after }B\) |
| \(E\) | \(:\) | \(\text{needs } C \text{ and } D\) |
| \(F\) | \(:\) | \(\text{after } E\) |
\(C\) and \(D\) meet at one event where \(E\) begins — no dummy needed.
| Activity | Immediate predecessor(s) |
|---|---|
| \(A\) | — |
| \(B\) | — |
| \(C\) | A, B |
| \(D\) | B |
| \(E\) | C, D |
Shared but unequal predecessors force a dummy.
| \(A,\ B\) | \(:\) | \(\text{start}\) |
| \(D\) | \(:\) | \(\text{needs } B \text{ only}\) |
| \(C\) | \(:\) | \(\text{needs } A \text{ and } B\) |
| \(\Rightarrow\ \text{dummy}\) | \(:\) | \(\text{carries } B \text{ into } C\) |
The dashed dummy gives \(C\) both predecessors while \(D\) keeps \(B\) alone.
Common pitfalls
Frequently asked questions
How do you draw a network diagram from a precedence table?
Draw every activity with a dash leaving a single start event, then attach each remaining activity so it leaves the event where all of its immediate predecessors finish. Add a dashed dummy if two activities share only some predecessors, then lead the last activities into a final event.
What is an immediate predecessor?
An immediate predecessor of an activity is an activity that must be completely finished before it can start. In an activity-on-edge network these are the arrows that enter the event where the activity begins.
What is a dummy activity and when do you need one?
A dummy activity is a dashed arrow that represents no real work and takes zero time. You add one when two activities share only some of their predecessors, so that each activity ends up depending on exactly the right earlier activities.
How can you tell the starting and finishing activities?
Starting activities are the arrows that leave the very first event and have no arrow entering it, so they have no predecessor. A finishing activity is an arrow that reaches the final event with nothing leaving after it. A project can have more than one starting or finishing activity.
How do you count the number of activities in a network?
Count the labelled arrows, not the numbered circles. The circles are events (points in time), while each directed arrow is one activity. Dashed dummy arrows are not counted as activities.